Understanding Tensors for General Relativity: A Comprehensive Guide

[BiGyElLoWhAt]

Hi all, I'm fairly new to GR, and I'm also somewhat new to tensors as well. I'm looking for some detailed explanation of a tensor, as I want to begin studying GR mathematically. I watched a video that was posted on PF not too long ago that was pretty good. I'm having trouble remembering who it was, but basically it took a cube and assigned 3-space vectors to each side, and each side was represented by a vector. I can see that as an explanation, but that doesn't let me start doing math with tensors. A link that starts with something like vector calculus and goes through tensor manipulation (algebra/calculus) (I'm assuming it's different than matrix algebra/calculus) would be ideal. Explanations are great as well. If a book is HIGHLY recommended I will go buy it, but I prefer to not work through books, it's hard to keep motivation for self study with a book for some reason.

I would say I have a reasonable conceptual understanding of tensors, but am looking into reworking through specific solutions of GR. In order to do so, I need a better understanding of tensors.

Any suggestions?
BYH

 

[Nugatory]

You might give this a try: http://preposterousuniverse.com/grnotes/grtinypdf.pdf

 

[jmatt]

Hello guy with the scary picture! I highly recommend https://www.amazon.com/dp/0957389442/?tag=pfamazon01-20 . It starts with a basic review of the math you need and gently leads you through everything! It helped me a lot before I tried more academic books.